Regularization methods are a key tool in the solution of inverse problems. They are used to
introduce prior knowledge and allow a robust approximation of ill-posed (pseudo-) inverses …

Regularization methods aimed at finding stable approximate solutions are a necessary tool
to tackle inverse and ill-posed problems. Inverse problems arise in a large variety of …

Total variation methods and similar approaches based on regularizations with ℓ 1-type
norms (and seminorms) have become a very popular tool in image processing and inverse …

This paper investigates the theoretical guarantees of ℓ^1-analysis regularization when
solving linear inverse problems. Most of previous works in the literature have mainly focused …

Regularization plays a pivotal role when facing the challenge of solving ill-posed inverse
problems, where the number of observations is smaller than the ambient dimension of the …

This paper studies least-square regression penalized with partly smooth convex
regularizers. This class of penalty functions is very large and versatile, and allows to …

The ℓ 1-synthesis model and the ℓ 1-analysis model recover structured signals from their
undersampled measurements. The solution of the former is a sparse sum of dictionary …

Variational sparsity regularization based on ℓ 1-norms and other nonlinear functionals has
gained enormous attention recently, both with respect to its applications and its …

In this paper, we consider using total variation (TV) minimization to recover signals whose
gradients have a sparse support, from a small number of measurements. We establish a …

We investigate compressed sensing (CS) techniques for reducing the number of
measurements in photoacoustic tomography (PAT). High resolution imaging from CS data …